The usual suspects, including the wealthy, the self-employed, those with offshore accounts, those with complex investment and business transactions, and those with anomalous returns.
Still, few audits are random. The primary method for selection is the IRS’ “Discriminant Information Function” (DIF). The DIF scores tax returns and the higher the score the more likely an audit and a resulting tax change on the return. Like the Big Mac special sauce and the ingredients in Coca Cola, the DIF is a trade secret. Although it is kept secret to prevent abuse, certain “red flags” are captured by the DIF. These “red flags” include unreasonable deductions in comparison to income, continued business losses, all or mostly “round” numbers on a return, incomplete returns, and significant fluctuations in income or deductions from year to year.
Your best defenses in avoiding an audit are to keep accurate records and to hire a reputable tax preparer. If selected for audit, you should consider legal representation.